Abstract
Hybrid control systems have shown strong evidence in both nature and engineering. Before the investigation of hybrid multi-agent networks, this chapter reviews the hybrid impulsive and switching control methods and their application to nonlinear systems. This chapter produces basic rules for designing hybrid impulsive and switching control that would be useful for the subsequent chapters.
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J. P. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube, “Impulse differential inclusions: A viability approach to hybrid systems,” IEEE Trans. on Automat. Contr., vol.47, no.1, pp.1–20, Jan. 2001.
D. D. Bainov and P. S. Simeonov, Stability Theory of Differential Equations with Impulse Effect: Theory and Applications. Chichester: Ellis Horwood, 1989.
D. Chen, J. Sun, and Q. Wu, “Impulsive control and its application to Lu’s chaotic system”, Chaos, Solitons & Fractals, vol.21, pp.1135–1142, 2004.
R. A. Decarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, “Perspective and results on the stability and stabilizability of hybrid systems,” Proc. IEEE, vol.88, pp.1069–1082, July, 2000.
Z. H. Guan, G. Chen, and T. Ueta, “On impulsive control of a periodically forced chaotic pendulum system,” IEEE Trans. on Automatic Control, vol.45, no.9, pp.1724–1727, Sep. 2000.
J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” in Proc. 38th Conf. Decision and Control, 1999, pp.2655–2660.
W. M. Haddad, V. Chellaboina, and N. A. Kablar, “Nonlinear impulsive dynamical systems, Part I, II, Int. J. Contr., vol.74, no.17, pp.1631–1677, 2001.
L. Huang, Linear Algebra in Systems and Control Theory, Beijing: Science Press, 1984, pp.211–214.
A. Khadra, X. Liu, and X. Shen, “Application of impulsive synchronization to communication security,” IEEE Trans. on Circuits and Systems, vol.50, no.3, pp.341–350, Mar. 2003.
S. Leela, F. A. McRae, and S. Sivasundaram, “Controllability of impulsive differential equations,” J. Math. Anal. Appl., vol.177, no.1, 1993.
Z. G. Li, C. B. Soh, and X. H. Xu, “Lyapunov stability for a class of hybrid dynamic systems,” Automatica, vol.36, pp.297–302, 2000.
Z. G. Li, Y. C. Soh, and C. Y. Wen, “Robust stability of a class of hybrid nonlinear systems,” IEEE Trans. on Automatic Control, vol.46, no.6, pp.897–903, June 2002.
Z. G. Li, C. Y. Wen, and Y. C. Soh, “Analysis and design of impulsive control systems”, IEEE Trans. on Automatic Control, vol.46, no.6, pp.894–897, June 2001.
Z. G. Li, Y. C. Soh, and C. Y. Wen, “Robust stability of quasi-periodic hybrid dynamic uncertain systems”, IEEE Trans. on Automatic Control, vol.46, no.1, pp.107–111, January 2001.
Z. G. Li, Y. C. Soh, and C. Y. Wen, “Stability of uncertain quasi-periodic hybrid dynamic systems”, Int. J. Control, vol.73, no.1, pp.63–73, 2000.
D. Liberzon, Switching in Systems and Control. Boston, MA : Birkhauser, 2003.
A. N. Michel, “Recent trends in the stability analysis of hybrid dynamical systems,” IEEE Trans. on Circuits and Systems, vol.46, no.1, pp.120–134, 1999.
T. Yang, Impulsive Control Theory, Berlin: Springer, 2001.
H. Ye, A. N. Michel, and L. Hou, “Stability theory for hybrid dynamical systems”, IEEE Trans. on Automatic Control, vol.43, no.4, pp.461–474, April, 1998.
G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives, and Applications, World Scientific Pub. Co., Singapore, 1998.
T. Ueta, H. Kawakami, and I. Morita, “A study of the pendulum equation with a periodic impulsive force–bifurcation and control,” IEICE Trans. Fundamentals, Vol.E78-A, pp. 1269–1275, 1995.
J. A. K. Suykens, T. Yang, J. Vandewalle, and L. O. Chua, “Impulsive control and synchronization of chaos,” in Controlling Chaos and Bifurcations in Engineering Systems, G. Chen (Ed.), CRC Press, Boca Raton, FL, USA, 1999, pp. 275–298.
S. G. Pandit and S. G. Deo, Differential Systems Involving Impulses. New York: Springer, 1982.
V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulse Differential Equations. Singapore: World Scientific, 1989.
Y. Q. Liu and Z. H. Guan, Stability, Stabilization and Control of Measure Large-Scale Systems with Impulses. Guangzhou: The South China University of Technology Press, 1996.
D. D. Bainov and P. S. Simeonov, Stability Theory of Differential Equations with Impulse Effect: Theory and Applications. Chichester: Ellis Horwood, 1989.
X. F. Wang and G. Chen, “Chaotification via arbitrarily small feedback controls: Theory, method, and applications,” Int. J. Bifurcation and Chaos, vol. 10, pp. 549–570, 2000.
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Guan, ZH., Hu, B., Shen, X.(. (2019). Hybrid Impulsive and Switching Control and Its Application to Nonlinear Systems. In: Introduction to Hybrid Intelligent Networks. Springer, Cham. https://doi.org/10.1007/978-3-030-02161-0_7
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DOI: https://doi.org/10.1007/978-3-030-02161-0_7
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